Percolation of entropy functionals on cayley tree graphs as a method of order-disorder character diagnostics of complex structures
Vitalii Vital'evich Yudin, Pavel Leonidovich Titov, A. N. Mikhalyuk · Bulletin of the Russian Academy of Sciences Physics · 2009
The problem of long-range action identification of classical quartet, honeycomb, and simplex lattices and bihexagonal Duneau-Katz lattice has been solved. The percolation problem is considered in terms of entropy functional on Cayley tree graphs. Long-range order is described not only by hyperbolic percolation entropy dependence with γ ≤ 1 and zero-order asymptotic entropy; the residual entropy of system ordering can also be observed in some cases.